Matrices- Variable in Matrices-Help

[Nikki16]

Matrices- Variable in Matrices-Help!

1-19-12
I need help. I have a homework question that I have tried to solve.
The matrix in the attachment has no inverse. Explain how you can determine the value of x. Then find x.

I tried cross multiplying.
3*2/3=4x
6/3=4x
2=4x
x=2/4
x=1/2

 

[Mark44]

1-19-12
I need help. I have a homework question that I have tried to solve.
The matrix in the attachment has no inverse. Explain how you can determine the value of x. Then find x.

I tried cross multiplying.
3*2/3=4x
6/3=4x
2=4x
x=2/4
x=1/2

There is no attachment.

 

[Nikki16]

It say it is attached now.

 

[Mark44]

1-19-12
I need help. I have a homework question that I have tried to solve.
The matrix in the attachment has no inverse. Explain how you can determine the value of x. Then find x.

I tried cross multiplying.
3*2/3=4x
6/3=4x
2=4x
x=2/4
x=1/2

The entry at the upper left is -3, not 3.

Why did you start by cross-multiplying? I'm looking for you to explain why you did what you did.

 

[Nikki16]

My teacher taught me in some cases involving variables we use cross multiplying. I have a textbook also that says so.

 

[micromass]

My teacher taught me in some cases involving variables we use cross multiplying. I have a textbook also that says so.

Yes, but did your teacher or book also explain why this technique works??

 

[Nikki16]

No neither did.

 

[micromass]

Do you know about determinants??

 

[Nikki16]

Yes. The thing is I am in 8th grade doing 11th grade honors Algebra 2.

 

[micromass]

Yes. The thing is I am in 8th grade doing 11th grade honors Algebra 2.

OK, what do determinants say about a matrix being invertible??

 

[Nikki16]

I do not know. I know the determinent is a real number that can be computed from elements by a specific formula.

 

[eumyang]

Just out of curiosity, what is the author and publisher of your book?

 

[genericusrnme]

do you understand what a matrix does?
what the span of a matrix is?
and if so, do you understand why a matrix would be singular?
it's better to understand what things actually do rather than to remember some rules about them

edit;

I do not know. I know the determinent is a real number that can be computed from elements by a specific formula.

I really dislike this way of teaching the subject (I only know from books, I've never had any formal education in maths), the determinant is an interesting little fellow with sets of properties which can give you information about the matrix when computed.
What you are doing when you do the cross multiplication is using one of these properties of the determinant, specifically one that gives information about the linear dependancy of the vectors in the c-space of the matrix which by extention tells you about it's invertibility.

I'll reffer you to an opencourseware lecture that MIT did;


That whole course is a pretty good introduction to linear algebra in general and Gilbert Strang is quite good at teaching imo.

 

[Mark44]

do you understand what a matrix does?
what the span of a matrix is?

I would guess that the OP isn't this far along in his/her studies of linear algebra.

and if so, do you understand why a matrix would be singular?
it's better to understand what things actually do rather than to remember some rules about them

edit;


I really dislike this way of teaching the subject (I only know from books, I've never had any formal education in maths), the determinant is an interesting little fellow with sets of properties which can give you information about the matrix when computed.
What you are doing when you do the cross multiplication is using one of these properties of the determinant, specifically one that gives information about the linear dependancy of the vectors in the c-space of the matrix which by extention tells you about it's invertibility.

More to the point, a square matrix is invertible (i.e., has an inverse) if and only if its determinant is nonzero. The concepts of vectors and linear dependence of the column space are likely too advanced for this poster, IMO.

I'll reffer you to an opencourseware lecture that MIT did;


That whole course is a pretty good introduction to linear algebra in general and Gilbert Strang is quite good at teaching imo.